Problem: $\dfrac{d}{dx}\left(x^{^{\scriptsize\dfrac{5}{3}}}\right)=$
Solution: The derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a fraction.) $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{^{\frac{5}{3}}}\right) \\\\ &=\dfrac{5}{3}x^{^{\frac{5}{3}-1}} \gray{\text{The power rule}} \\\\ &=\dfrac53x^{^{\frac{2}{3}}} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(x^{^{\frac{5}{3}}}\right)=\dfrac53x^{^{\frac{2}{3}}}$. This can also be written as ${\dfrac53}{\sqrt[3]{x^2}}$ (all equivalent forms are accepted).